Electronic band structure | EPFL Graph Search

In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules. Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption, and forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.). Why bands and band gaps occur The electrons of a single, isolated atom occupy atomic orbitals each of which has a discrete energy level. When two identical atoms join to form a molecule, their atomic orbitals overlap. Since electrons are fermions, the Pauli exclusion principle prohibits them from havi

A theoretical study of disorder and decomposition in multinary nitrides hard coatings materials

Björn Alling

The development of multinary nitrides materials has revolutionised the hard coatings industry over the last 20 years. Especially important materials systems in this matter have been TiAlN and CrAlN which shows higher hardness, better oxidation resistance and can perform at higher temperatures as compared to TiN. When synthesised through physical vapour deposition techniques these system form cubic rock salt structured Ti1-xAlxN and Cr1-xAlxN solid solutions as a metastable phase over a large part of the concentration range. One of the main objectives during the optimisation of the coatings has been to increase the amount of Al in the coating while still keeping the rock salt structure, avoiding phase separation and the formation of hexagonal wurtzite AlN. However, in Al-rich TiAlN coatings it was found that isostructural decomposition within the cubic phase was in fact beneficial for the coatings performance at working temperatures just below 1000 °C. The reason was that the formation of strained coherent c-AlN domains within the grains initiated a age-hardening of the coating. In the CrAlN coatings it is possible to solve a larger amount of Al in the cubic phase. Possibly connected to this fact is that no isostructural decomposition and in principle no age hardening has been observed in rock salt structured Cr1-xAlxN. Although large series of experimental investigations have been performed on these systems, no systematic theoretical study has yet been undertaken. This theoretical work is an attempt by means of first-principles calculations together with thermodynamics considerations within the framework of alloy theory, to close or decrease the knowledge gap between experimental observations of cutting performance of various coatings and the fundamental quantum mechanical and thermodynamics processes that governs it. We first consider the structural properties of the treated mixed nitride systems. The concept of atomic misfit or volume difference, which is well known in the community is studied and the physics that leads to a positive deviation from Vegard's rule is revealed. Then the TiAlN and CrAlN systems are studied in detail. A clear connection between the development of the electronic structure with composition and the mixing enthalpy of the alloys, and thus the tendency for decomposition, is found for TiAlN. The importance of magnetic effects on the thermodynamics of mixing in CrAlN is established leading to a qualitative lower tendency for decomposition. Since the nitrogen composition can deviate substantially from perfect stoichiometry in these systems, a study of the influence of nitrogen vacancies on the decomposition pattern of TiAlN in the cubic phase is performed. The results imply that a presence of nitrogen sub-stoichiometry in Al-rich TiAlN will enhance the tendency for isostructural decomposition. The achieved results including those for the systems ScAlN and HfAlN are compared and discussed especially by considering volume misfit and electronic bandstructure effects as driving forces for coherent and incoherent decomposition.

EPFL2009

Influence of static correlation on the magnon dynamics of an itinerant ferromagnet with competing exchange interactions: First-principles study of MnBi

Henrik Moodysson Rønnow, Thorbjørn Skovhus

We present first-principles calculations of the dynamic susceptibility in strained and doped ferromagnetic MnBi using time-dependent density functional theory. In spite of being a metal, MnBi exhibits signatures of strong correlation and a proper description in the framework of density functional theory requires Hubbard corrections to the Mn d orbitals. To permit calculations of the dynamic susceptibility with Hubbard corrections applied to the ground-state electronic structure, we use a consistent rescaling of the exchange-correlation kernel maintaining the delicate balance between the magnon dispersion and the Stoner continuum. We find excellent agreement with the experimentally observed magnon dispersion for pristine MnBi and show that the material undergoes a phase transition to helical order under application of either doping or strain. The presented methodology paves the way for future linear response time-dependent density functional theory studies of magnetic phase transitions, also for the wide range of materials with pronounced static correlation effects that are not accounted for at the local density approximation level.

AMER PHYSICAL SOC2022

Magnonic crystals with reconfigurable magnetic defects for spin-based microwave electronics

Korbinian Baumgärtl

Collective spin excitations can propagate in magnetically ordered materials in the form of waves. These so-called spin waves (SWs) or magnons are promising for low-power beyond-CMOS information processing, which does not rely anymore on the lossy movement of electric charges. SWs in the few GHz frequency regime possess nanoscale wavelengths about five orders of magnitude smaller than electromagnetic waves of the same frequency. This property makes SWs ideally suited for application in microwave technology, essential for on-chip processing of wireless telecommunication signals. In this thesis, three crucial challenges relevant for the technological application of SWs are addressed: First, to functionalize SWs and exploit their small wavelengths, it is necessary to control them at the nanoscale. Here, periodically nanostructured materials, denoted magnonic crystals, are promising, as they allow to tailor the band structure of SWs. We report on SWs propagating in a prototypical one-dimensional magnonic crystal consisting of dipolarly coupled magnetic nanostripes. The remanent magnetization of individual stripes was designed to be bistable along the long axis. By magnetizing an individual stripe in opposite direction to the others, we created a magnetic defect. We measured by means of all-electrical spin wave spectroscopy and Brillouin light scattering microscopy phase and amplitude of SWs trespassing the defect. We found that SW phases and amplitudes were modified at the nanoscale, and phase shifts could be tuned by an applied bias magnetic field. Using micromagnetic simulations, we identified specific bias fields for which phase shifts of Pi are achieved without suppressing SW amplitudes. This result is highly relevant for the implementation of logic gates based on interference of phase-controlled SWs. We further measured propagation of short-waved SWs in an antiferromagnetically ordered one-dimensional magnonic crystal, where every second stripe was magnetized in opposite direction. We found a band gap closing at the Brillouin zone boundary when no magnetic bias field was applied. Our observations are promising for reprogrammable microwave filters capable of adjusting stop- and passband. Second, we address how long-waved electromagnetic waves can be coupled efficiently to nanoscale SWs. We demonstrate by space- and time-resolved scanning X-ray transmission measurements, that excited nanogratings allow to transfer their reciprocal lattice vector and multiple of it to an underlying magnetic thin film, in which nanoscale propagating SWs are launched. Additionally, we discovered a second method for short-waved SW generation based on magnetic microwave guides. This approach is easy to fabricate and relies on the adaption of the SW wavelength to a changing effective magnetic field. Efficient coupling of electromagnetic waves to nanoscale SWs promises an unprecedented miniaturization of microwave components. Third, we found that the magnetization direction of bistable nanomagnets can be switched by propagating SWs in an underlying magnetic thin film when a threshold amplitude is reached. This discovery is promising for the realization of a non-volatile magnonic memory, which stores SW amplitudes. A possible application are SW logic gates, which encode the outcome of a logic operation in the output SW amplitude. Magnonic memory would allow for storing these amplitudes directly, without requiring lossy conversion into the electrical domain.

EPFL2021